Bouganis, A. (2014) 'Non-abelian p-adic L-functions and Eisenstein series of unitary groups - the CM method.', Annales de l'Institute Fourier., 64 (2). pp. 793-891.
In this work we prove various cases of the so-called “torsion congruences” between abelian p-adic L-functions that are related to automorphic representations of definite unitary groups. These congruences play a central role in the non-commutative Iwasawa theory as it became clear in the works of Kakde, Ritter and Weiss on the non-abelian Main Conjecture for the Tate motive. We tackle these congruences for a general definite unitary group of n variables and we obtain more explicit results in the special cases of n = 1 and n = 2. In both of these cases we also explain their implications for some particular “motives”, as for example elliptic curves with complex multiplication. Finally we also discuss a new kind of congruences, which we call “average torsion congruences”.
|Keywords:||p-adic, L-functions, Eisenstein Series, Unitary Groups, Congruences.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.5802/aif.2866|
|Date accepted:||17 January 2014|
|Date deposited:||28 January 2015|
|Date of first online publication:||02 December 2014|
|Date first made open access:||No date available|
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